Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems (Springer Series in Computational Mathematics, 14) 2nd Edition by Ernst Hairer (PDF)

Description

The subject of this book is the solution of stiff differential equations and of differential-algebraic systems. This second edition contains new material including new numerical tests, recent progress in numerical differential-algebraic equations, and improved FORTRAN codes.From the reviews:”A superb book…Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text.” –MATHEMATICS TODAY

User’s Reviews

Editorial Reviews: Review From the reviews of the second edition:This is a superb book…Throughout, illuminating graphics, sketches and quotes from papers of researchers in the field add an element of easy informality and motivate the text.” Mathematics Today“This volume, on nonstiff equations, is the second of a two-volume set. This second volume treats stiff differential equations and differential-algebraic equations. … This book is highly recommended as a text for courses in numerical methods for ordinary differential equations and as a reference for the worker. It should be in every library, both academic and industrial.” (Teodora-Liliana Rădulescu, Zentralblatt MATH, Vol. 1192, 2010) From the Back Cover The subject of this book is the solution of stiff differential equations and of differential-algebraic systems (differential equations with constraints). There is a chapter on one-step and extrapolation methods for stiff problems, another on multistep methods and general linear methods for stiff problems, a third on the treatment of singular perturbation problems, and a last one on differential-algebraic problems with applications to constrained mechanical systems. The beginning of each chapter is of introductory nature, followed by practical applications, the discussion of numerical results, theoretical investigations on the order and accuracy, linear and nonlinear stability, convergence and asymptotic expansions. Stiff and differential-algebraic problems arise everywhere in scientific computations (e.g. in physics, chemistry, biology, control engineering, electrical network analysis, mechanical systems). Many applications as well as computer programs are presented.Ernst Hairer and Gerhard Wanner were jointly awarded the 2003 Peter Henrici Prize at ICIAM 2003 in Sydney, Australia.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is crucial for understanding the techniques that apply to numerically integrating differential equations. There are only a couple of other books that deal with this topic as of the end of 2014. It provides a number of formulas for ERK (Explicit Runge-Kutta) formulas that have been optimized for a good balance between stability and accuracy, and gives an example how to calculate a step size to stay within these formulas reach. There are also a number of IRK (Implicit Runge-Kutta) formulas that have been derived for either conservation (where the total energy of a system must not increase or decrease) or higher degree of formula per stage.A-stability, L-stability, and A(alpha) stability are covered and examples of deriving the stabilities of all of the presented formulas are given. The authors discuss the derivation of both ERK and IRK formulas, and then go onto discuss DIRK (Diagonally Implicit) and Stiffly accurate (SDIRK) methods. Order stars are discussed, and there are shown equivalent analyses to order stars that I don’t know how to describe.The above is just the first 1/4th of the book, and is all I’ve been able to look at. I highly, highly recommend this book.

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